Simplify the following expression: $\dfrac{3x^2}{9x^5}$ You can assume $x \neq 0$.
$ \dfrac{3x^2}{9x^5} = \dfrac{3}{9} \cdot \dfrac{x^2}{x^5} $ To simplify $\frac{3}{9}$ , find the greatest common factor (GCD) of $3$ and $9$ $3 = 3$ $9 = 3 \cdot 3$ $ \mbox{GCD}(3, 9) = 3 $ $ \dfrac{3}{9} \cdot \dfrac{x^2}{x^5} = \dfrac{3 \cdot 1}{3 \cdot 3} \cdot \dfrac{x^2}{x^5} $ $\phantom{ \dfrac{3}{9} \cdot \dfrac{2}{5}} = \dfrac{1}{3} \cdot \dfrac{x^2}{x^5} $ $ \dfrac{x^2}{x^5} = \dfrac{x \cdot x}{x \cdot x \cdot x \cdot x \cdot x} = \dfrac{1}{x^3} $ $ \dfrac{1}{3} \cdot \dfrac{1}{x^3} = \dfrac{1}{3x^3} $